Neumann and Bargmann systems associated with an extension of the coupled KdV hierarchy

An eigenvalue problem with a reference function and the corresponding hierarchy of nonlinear evolution equations are proposed. The bi-Hamiltonian structure of the hierarchy is established by using the trace identity. The isospectral problem is nonlinearized as to be finite-dimensional completely integrable systems in Liouville sense under Neumann and Bargmann constraints

Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator.We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed. A direct result is that the $n$-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.Comment: 12 pages, 0 figur

Thermodynamic properties in the normal and superconducting states of Na(x)CoO(2)*yH(2)O powder measured by heat capacity experiments

The heat capacity of superconducting Na(x)CoO(2)*yH(2)O was measured and the data are discussed based on three different models: The thermodynamic Ginzburg-Landau model, the BCS theory, and a model including the effects of line nodes in the superconducting gap function. The electronic heat capacity is separated from the lattice contribution in a thermodynamically consistent way maintaining the entropy balance of superconducting and normal states at the critical temperature. It is shown that for a fully gapped superconductor the data can only be explained by a reduced (about 55 %) superconducting volume fraction. The data are compatible with 100 % superconductivity in the case where line nodes are present in the superconducting gap function.Comment: Revised, 19 pages, 3 figure

Topology design for fast convergence of network consensus algorithms

The quantities of coefficient of ergodicity and algebraic connectivity have been used to estimate the convergence rates of discrete-time and continuous-time network consensus algorithms respectively. Both of these two quantities are defined with respect to network topologies without the symmetry assumption, and they are applicable to the case when network topologies change with time. We present results identifying deterministic network topologies that optimize these quantities. We will also propose heuristics that can accelerate convergence in random networks by redirecting a small portion of the links assuming that the network topology is controllable.

A perturbative approach to non-Markovian stochastic Schr\"odinger equations

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two level atom immersed in a environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensembled average state $\rho_{\rm red}(t)$ approach the exact reduced state found via Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].Comment: 17 pages, 4 figure

A Possible Crypto-Superconducting Structure in a Superconducting Ferromagnet

We have measured the dc and ac electrical and magnetic properties in various magnetic fields of the recently reported superconducting ferromagnet RuSr2GdCu2O8. Our reversible magnetization measurements demonstrate the absence of a bulk Meissner state in the compound below the superconducting transition temperature. Several scenarios that might account for the absence of a bulk Meissner state, including the possible presence of a sponge-like non-uniform superconducting or a crypto-superconducting structure in the chemically uniform Ru-1212, have been proposed and discussed.Comment: 8 pages, 5 PNG figures, submitted to Proceedings of the 9th Japan-US Workshop on High-Tc Superconductors, Yamanashi, Japan, October 13-15, 1999; accepted for publication in Physica C (December 24, 1999

Evidence for Possible Phase-Separations in RuSr2(Gd,Ce)2Cu2O10-delta

An unusual thermal-magnetic hysteresis was observed between a minor magnetic transition around 120 K and the main one at 80 K in superconducting RuSr2(R,Ce)2Cu2O10-delta (Ru1222R) samples, where R = Gd or Eu, down to a submicron length-scale. The observation suggests a possible phase-separation and is consistent with the very small but universal demagnetizing factor observed, which is difficult to reconcile with the canted spin-structure previously proposed. In such a scenario, the unusual superconducting properties of the Ru-based cuprates can also be understood naturally.Comment: 8 pages, 3 figures, submitted to Phys. Rev. B, "Rapid Communications" (September 26, 2001

Z decays into light gluinos: a calculation based on unitarity

The Z boson can decay to a pair of light gluinos through loop-mediated processes. Based on unitarity of the S-matrix, the imaginary part of the decay amplitude is computed in the presence of a light bottom squark. This imaginary part can provide useful information on the full amplitude. Implications are discussed for a recently proposed light gluino and light bottom squark scenario.Comment: 19 pages, LaTeX, 3 figures, submitted to Phys. Rev.

Growth evolution and formation mechanism of η ′-Cu 6 Sn 5 whiskers on η -Cu 6 Sn 5 intermetallics during room-temperature ageing

Abstract(#br)The phase-transformation-induced damage of Cu 6 Sn 5 is an emerging reliability issue in the manufacturing of 3D ICs. Although the retarded phase transformation from η -Cu 6 Sn 5 to η ′-Cu 6 Sn 5 at room temperature can produce a large expansion in volume, how the transformation stress threatens the joint reliability during usage is poorly understood. In this paper, the evolution characteristics of quenched η -Cu 6 Sn 5 bumps were observed during ageing at 25 °C for 1–40 d Due to the retarded phase transformation, η ′-Cu 6 Sn 5 whiskers spontaneously nucleated and grew on the surfaces of η -Cu 6 Sn 5 bumps. The orientation relationship between the two phases favourable for whisker growth was confirmed, and two necessary conditions for whisker formation were discussed. In addition, the potential harmfulness of whisker growth was analysed. The study will help expose the phase-transformation-induced damage of Cu 6 Sn 5 during room-temperature ageing and may reduce the failure risk of entire Cu 6 Sn 5 intermetallic joints in future large-scale applications of 3D ICs